Blender function to transform a selected edge along a custom axis
I think http://web.purplefrog.com/~thoth/blender/python-cookbook/extrude-edge-along-custom-axis.html will accomplish your mission.  Here's a copy in-line:

import bpy
import bmesh


def guess_edge_order(bm, edge):
    """ We need to create a new face,
    but if that face is going to have a normal consistent with an adjacent face
    we need to choose the order of the vertices carefully.
    """
    v0 = edge.verts[0]
    v1 = edge.verts[1]
    if len(edge.link_faces) != 1:
        # it is going to be non-manifold.  balls!
        return v0, v1

    face = edge.link_faces[0]
    nverts = len(face.verts)

    i0 = [ i for i in range(nverts) if face.verts[i].index == v0.index]
    i0 = i0[0]
    #print(["indices", i0, face.verts[i0], face.verts[i1], i1])
    i1 = (i0 + 1)% nverts
    #print(["next", face.verts[i1] , "==", v1])

    # does the polarity of this edge match the order of the vertices on the face?
    if (face.verts[i1].index != v1.index):
        return v0, v1
    else:
        return v1,v0


def mission1(obj, axis, len):

    bm = bmesh.from_edit_mesh(obj.data)

    # collect a set of all the vertices from all selected edges (without duplicates)
    verts = set()
    for edge in bm.edges:
        if edge.select:
            verts.add(edge.verts[0])
            verts.add(edge.verts[1])
    print(verts)

    # create new vertices "extruded" from the vertices of all the selected edges and
    # stash them in a hash so we can map from the old vertex to its extruded partner
    newverts = {}
    for v in verts:
        v2 = bm.verts.new( v.co + axis*len)
        newverts[v.index] = v2

    # for each selected edge create a new face from the original edge plus the extruded vertices
    for edge in bm.edges:
        if edge.select:
            v0,v1 = guess_edge_order(bm, edge)
            v2 = newverts[v1.index]
            v3 = newverts[v0.index]
            bm.faces.new( [v0, v1, v2, v3] )

    # if we don't do this, it will look silly in the editor, and maybe even cause problems during render
    bm.normal_update()

    # apply all the changes we made back to to the target mesh data
    bmesh.update_edit_mesh(obj.data, destructive=True)

#
#
#

obj = bpy.context.active_object
scn = bpy.context.scene
# which custom orientation are we using?
orientation = scn.orientations['Face']

x_axis=0
y_axis=1
z_axis=2
m1 = obj.matrix_world.to_3x3().inverted() # this is what we need to map from world space to object space
m2 = orientation.matrix.transposed() # we transpose this so we can extract a column
global_axis = m2.row[z_axis] # this is the custom orientation axis we want in global space
axis = m1* global_axis # now we have the necessary extrusion vector in the object's local coordinate space

if True:
    print (m1*m2.row[x_axis])
    print (m1*m2.row[y_axis])
    print (axis)

mission1(obj, axis, 1.5)